x = 13. We solve this Alternatively, by drawing.

In total, Betty drove 5 miles west (8-3) and 12 miles north (6+6).
Drawign a straight line from her start to end point, this is the hypotenuse of a right triangle with sides 12 and 5. using pytahgoras: x^2=12^2+5^2=144+25+169. x = 13.

We can sketch the situation as follows:

We want to find the value of x

Draw an auxiliary line that's perpendicular to the bottom line:


From here, we can see we have a blue RIGHT triangle, with legs of length 5 and 12


To find the value of x, we might recognize that 5 and 12 are two of the three lengths in the Pythagorean Triplet 5-12-13
So, the hypotenuse has length 13

Alternatively, we can apply the Pythagorean Theorem.
We get: 5² + 12² = x²
Simplify: 25 + 144 = x²
Simplify: 169 = x²
Solve: x = √169 = 13

Answer: 13

Cheers,
Brent

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